Is there any specific SW framework, libraries or algorithms (supported by any theory) designed for implementing a practical AGI system?
Not to my knowledge. The problem is that this is such an enormous task, it cannot really be tackled at once. So the obvious solution is to reduce the scope. In early AI people were using toy domains, whereas nowadays AI systems work more generally (but still perform better if the domain is restricted).
So while (slow) progress is being made putting the individual building blocks together, we're still a long way off building an overarching general system from them.